222 research outputs found
Approximate Bayesian Computational methods
Also known as likelihood-free methods, approximate Bayesian computational
(ABC) methods have appeared in the past ten years as the most satisfactory
approach to untractable likelihood problems, first in genetics then in a
broader spectrum of applications. However, these methods suffer to some degree
from calibration difficulties that make them rather volatile in their
implementation and thus render them suspicious to the users of more traditional
Monte Carlo methods. In this survey, we study the various improvements and
extensions made to the original ABC algorithm over the recent years.Comment: 7 figure
A Simple Approach to Maximum Intractable Likelihood Estimation
Approximate Bayesian Computation (ABC) can be viewed as an analytic
approximation of an intractable likelihood coupled with an elementary
simulation step. Such a view, combined with a suitable instrumental prior
distribution permits maximum-likelihood (or maximum-a-posteriori) inference to
be conducted, approximately, using essentially the same techniques. An
elementary approach to this problem which simply obtains a nonparametric
approximation of the likelihood surface which is then used as a smooth proxy
for the likelihood in a subsequent maximisation step is developed here and the
convergence of this class of algorithms is characterised theoretically. The use
of non-sufficient summary statistics in this context is considered. Applying
the proposed method to four problems demonstrates good performance. The
proposed approach provides an alternative for approximating the maximum
likelihood estimator (MLE) in complex scenarios
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